Summary:
In this lesson we will be learning about midpoints and bisectors. By the end of this lesson you will know how to calculate a midpoint and how to find a bisector. There are two ways to find the midpoint. When you have the two coordinates or when it is given and you have to find the endpoint. A bisector can be used in a segment or and angle, mainly we will be focusing on angles.
Find in textbook pages: 34-340
Vocabulary:
Midpoint: of a segment is the point that divides equally
Bisects: a point that divides the segment into two congruent segments
Segment bisector: a segment, ray, line, or plane that intersects a segment at its midpoint
Midpoint formula: an equation that allows you to find the mid point with two sets of coordinates. Formula: Midpoint: (x1+x2/2, y1+y2/2)
Angle bisectors: a ray that divides an angle into two adjacent angles that are congruent
Example 1:
Find the coordinates for the midpoint of segment AB, with the endpoints of A (-2,3) and B (5, -2).
Solution:
M= (-2+5/2, 3+ -2/2)
M= (3/2, ½)
Example 2:
The midpoint of RP is M (2,4). One of the endpoints R (-1,7). Find the coordinates of the other endpoint.
Solution: Because (2,4) is the midpoint you make them into two separate equations. You would have the x coordinates equal 2 and the y coordinates equal 4.
(2,4)= (-1+x/2, 7+y/2)
2= -1+x/2 4=7+y/2
4= -1+x 8= 7+y
5= x 1=y
P (5,1)
Example 3:
In the diagram ray RQ bisects angle PRS. The measure of the two congruent angles are (x+40) degrees and (3x-20). Solve for x.
In this lesson we will be learning about midpoints and bisectors. By the end of this lesson you will know how to calculate a midpoint and how to find a bisector. There are two ways to find the midpoint. When you have the two coordinates or when it is given and you have to find the endpoint. A bisector can be used in a segment or and angle, mainly we will be focusing on angles.
Find in textbook pages: 34-340
Vocabulary:
Midpoint: of a segment is the point that divides equally
Bisects: a point that divides the segment into two congruent segments
Segment bisector: a segment, ray, line, or plane that intersects a segment at its midpoint
Midpoint formula: an equation that allows you to find the mid point with two sets of coordinates. Formula: Midpoint: (x1+x2/2, y1+y2/2)
Angle bisectors: a ray that divides an angle into two adjacent angles that are congruent
Example 1:
Find the coordinates for the midpoint of segment AB, with the endpoints of A (-2,3) and B (5, -2).
Solution:
M= (-2+5/2, 3+ -2/2)
M= (3/2, ½)
Example 2:
The midpoint of RP is M (2,4). One of the endpoints R (-1,7). Find the coordinates of the other endpoint.
Solution:
Because (2,4) is the midpoint you make them into two separate equations. You would have the x coordinates equal 2 and the y coordinates equal 4.
(2,4)= (-1+x/2, 7+y/2)
2= -1+x/2 4=7+y/2
4= -1+x 8= 7+y
5= x 1=y
P (5,1)
Example 3:
In the diagram ray RQ bisects angle PRS. The measure of the two congruent angles are (x+40) degrees and (3x-20). Solve for x.
X+ 40= 3x-20
40= 2x-20
60= 2x
30= x
Review Problems:
1) X (0,0)
Y (-8,6)
2) X (10,8)
Y (-2,5)
3) Angle ABD: 2x+35 and angle CBD: 5x-22
4) Angle ABD: 1/2x+20 and angle CBD: 3x-85
Helpful Websites to get more lessons:
- for a segment bisector:
http://www.icoachmath.com/SiteMap/SegmentBisector.html
- segment bisector video
http://www.watchknow.org/Video.aspx?VideoID=20214
- - midpoint example
http://www.youtube.com/watch?v=bcp9pJxaAOk
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